Quantum Foundations

A very general way of describing the abstract structure of quantum theory is to say that the set of observables on a quantum system form a C*-algebra.  A natural question is then, why should this be the case - why can observables be added and multiplied together to form any algebra, let alone of the special C* variety?  I will present recent work with Markus Mueller and Howard Barnum, showing that the closest algebraic cousins to standard quantum theory, namely the Jordan-algebras, can be characterized by three principles having an informational flavour, namely: (1) a generalized spectral d

It is certainly possible to express ordinary quantum mechanics in the framework of a real vector space: by adopting a suitable restriction on all operators--Stueckelberg’s rule--one can make the real-vector-space theory exactly equivalent to the standard complex theory.  But can we achieve a similar effect without invoking such a restriction?  In this talk I explore a model within real-vector-space quantum theory in which the role of the complex phase is played by a separate physical system called the ubit (for “universal rebit”).  The ubit is a single binary real-vector-space quantum obje

The distinction between a realist interpretation of quantum theory that is psi-ontic and one that is psi-epistemic is whether or not a difference in the quantum state necessarily implies a difference in the underlying ontic state. Psi-ontologists believe that it does, psi-epistemicists that it does not. This talk will address the question of whether the PBR theorem should be interpreted as lending evidence against the psi-epistemic research program.

One of the most important open problems in physics is to reconcile quantum mechanics with our classical intuition. In this talk we look at quantum foundations through the lens of mathematical foundations and uncover a deep connection between the two fields. We show that Cantorian set theory is based on classical concepts incompatible with quantum experiments. Specifically, we prove that Zermelo-Fraenkel axioms of set theory (and the background classical logic) imply a Bell-type inequality.